You mentioned some very relevant details in your question, which are important to address. You stated that your mother hums a child's song and that it seems to make her happy. A possible interpretation of this behavior is that your mother is experiencing regression, a function of returning to an earlier time in her life that may have been happier or more pleasant. Singing a song from her childhood may envelop her with the memories and emotions that she experienced as a kid. By allowing her to reflect and reminisce on these times, you can help lift her spirits, which could ultimately increase her quality of life. In addition, she could be using this humming as a self-soothing mechanism. If she is feeling sad or frustrated, humming a happy tune can actually provide a way for her to help herself. This can be extremely effective because she may be able to rely on herself more instead of seeking gratification from others.

It is understandable if you are frustrated by your mother's frequent humming, but perhaps you can use it as an opportunity to refocus her on something else that could make her happy. The fact that your mother can still talk is very important, and you should use that to your advantage. When your mother starts humming, you can open up a conversation focused around the song itself. Compliment her on the tune, and ask her if she remembers the words, or who sang that song. If, for example, your mother says "Frank Sinatra," you can quickly redirect the discussion by bringing up memories during the days of Frank Sinatra, or anything that you think would be relevant to her. This will not only pause the humming, but allow her to put those innermost feelings into words. By talking about her memories, your mom can reconnect with her past just as effectively, and exercise her verbal abilities in the meanwhile.